Bridged t phase shifter



Feb. 12, 1952 P. H. RICHARDSON 2,585,841

BRIDGED T PHASE SHIFTER Fi led Sept. 22, 1949 z Sheets-Sheet 1 DEGREES lNl EN TOP 1? H. RICHARDSON ATTORNEY Feb. 12, 1952 R ON 2,585,841

v BRIDGED T PHASE SHIFTER.

Filed Sept. 22, 1949 I 3 Sheets-Sheet 2 FIG. .9 FIG. /0 W r22 2 1 z/ //v l EN TOR I? H RICHARDSON ATTORNEY 1952 P. H. RICHARDSON 2,585,8 1

I BRIDGED T PHASESHIFTER Filed Sept. 22, 1949 I 5 Sheets-Sheet 3 FIG. /5

' ATTORNEY Patented Feb. 12, 1952 BRIDGED 'r PHASE SHIFTER.

Paul H. Richardson, Chatham, N. J., assignor to Bell Telephone Laboratories, Incorporated, New York, N. Y., a corporation of New York Application September 22, 1949, Serial No. 117,255

23 Claims.

This invention relates to wave transmission networks and more particularly to variable phase shifters.

An object of the invention is to vary the phase shift of a wave transmission network over a wide range without changing its image impedance.

Another object is to maintain a constant insertion loss at all settings of such a phase shifter.

Other objects are to simplify the circuit and reduce the size and cost of phase shifters of this type.

There is often required a wave transmission network in which the phase shift at a single frequency may be varied without changing the insertion loss or the image impedance. Such a device may be built in the form of a constant-resistance structure but, in order to keep the image impedance constant, both variable inductors and variable capacitors are required.

The variable phase shifter of the present invention has the advantage that only a single type of variable reactor, either a capacitor or an inductor, is required. In the unbalanced form only two variable reactors are required and their reactances are equal at each setting. The circuit is of the bridged-T type. It is derived from a constant-resistance, all-pass, lattice network in which one branch comprises a general reactive impedance and the other branch comprises an equal impedance connected to the remote end of a subsidiary network which has a phase shift of 90 de rees or an odd multiple thereof at the operating frequency f and thus effects an inversion of the impedance. The subsidiary network may, for example, be a T or 1r of reactances forming a low-pass or a high-pass filter. In order to provide a wide range of phase shift, in one embodiment the general impedance includes both a capacitor and an inductor, connected either in series or in parallel, one of which is variable. To facilitate the transformation from lattice to bridged-T, one or more additional reactors may be added arbitrarily to the general impedance. By a special procedure the lattice may be transformed into an equivalent bridged-T network in which exactly equal variable reactances appear in both the bridging branch and the shunt branch. Since these variable reactremain equal at all settings of the phase shifter they may conveniently be arranged for unitary control. In order to maintain the insertion loss substantially constant at all settings, compensating resistors may be added to the bridging and shunt branches.

The nature of the invention will be more fully understood from the following detailed description and by reference to the accompanying drawing, in which like reference characters are used to designate similar or corresponding parts and of which:

Fig. 1 is a schematic circuit of the prototype constant-resistance lattice network in which the series branch is a general impedance ZA and the diagonal branch ZB comprises a second impedance ZA associated with a subsidiary impedance inverting network N;

Figs. 2 and 3 show the branch ZB when the network N is a ir-type low-pass or high-pass filter, respectively Fig. 4 shows a series type of general impedance ZA suitable for use with the vr-type networks N of Figs. 2 and 3;

Figs. 5 and 6 show diagonal branches ZB comprising T-type filters;

Fig. 7 shows a parallel type of general impedance ZA suitable for use with the T-type networks N of Figs. 5 and 6;

Fig. 8 is a schematic circuit of a bridged-T network equivalent, except for an interchange of branches, to the prototype lattice of Fig. 1 when the subsidiary network N is a 1r-type lowpass filter as shown in Fig. 2 and the general impedance ZA is the series type shown in Fig. 4;

Fig. 9 is a network similar to the one shown in Fig. 8 except that the high-pass filter of Fig. 3 is substituted for the low-pass filter;

Fig. 10 is a bridged-T network equivalent to the lattice of Fig. 1 when N is a T-type low-pass filter as shown in Fig. 5 and ZA is the parallel type of Fig. 7;

Fig. 11 is a network similar to the one shown in Fig. 10 except that the high-pass filter of Fig. 6 is substituted for the low-pass filter;

Fig. 12 is a circuit equivalent to the one shown in Fig. 8 after a portion of the bridging branch has undergone an impedance transformation to provide equal variable impedances 2/2 in the bridging and shunt branches;

Fig. 13 is a preferred embodiment of the invention, equivalent at the operating frequency f0 to the circuit of Fig. 12, in which one of the capacitors C in the bridging branch has been eliminated;

Figs. 14, 15 and 16 are other preferred embodiments derived, respectively, from the circuits shown in Figs. 9, 10 and 11;

Figs. 17, 18, 19 and 20 are specific circuits corresponding, respectively, to those shown in Figs.

3 13, 14, 15 and 16 when the variable impedance Z is constituted by the series combination of the elements L1, C1 and R1 in parallel with a compensating resistor R2, as shown in Fig. 21; and

Fig. 22 is a curve showing how the insertion phase shift of the network is related to the value of the variable reactance.

Taking up the figures in more detail, Fig. 1 shows schematically the prototype lattice network comprising two equal generalized series impedance branches ZA and a pair of equal diagonal impedances ZB connected between a pair of input terminals 1, 2 and a pair of output terminals 3, 4. Only one series branch ZA and one diagonal impedance ZB are shown explicitly, the

other corresponding branches being indicated by the broken lines connecting the appropriate terminals. A suitable source of alternating electromotive force may be connected to the input terminals and a load or utilization circuit connected to the output terminals.

The impedance Z3 is made up of a reactive four-terminal subsidiary network N connected to the diagonal branch at the terminals 5, 6 and terminated at its output terminals '7, 8' in an impedance ZA of the same value as the impedance forming the series branch of the lattice. The function of the subsidiary network N is to invert the impedance ZA with respect to Rt, the image impedance of the lattice, and therefore N also has an image impedance equal to R0 and an image phase constant which. is equal to an odd multiple of 90 degrees.

If the impedance ZA is essentially a. pure reactance of value XA the lattice network will operate as a phase shifter having an image impedance Rb and aninsertion phase shift {3 given y 3:2 tan- It is seen, therefore, that the phase shift introduced depends upon the reactance of the impedances ZA and may be varied by adjusting the value of XA- As will be explained below; the effects of' parasitic dissipation in the reactive elements forming ZA can be compensated for to a large extent, so that the insertion loss of the lattice is substantially constant and independent of the value of XA- Fig. 2 shows the configuration of the branch Ze when the network N is a 1r-type low-pass filter comprising a series inductance L with a shunt capacitance C connected at each end thereof. In order for the network N to have an insertion phase shift of '90 degrees at the operating frequency ,fo the elements have the following values:

C farads 1 foRo L=f henries (3) Fig. 3-shows the branch ZB when N is a 1r-type high-pass filter made upof a series capacitance C. and two shunt. inductances L, the values of which are given by Equations 2 and 3..

Fig. 4 shows a specific form of the impedance Z. suitable for use with the 1rtype networks of Figs. 2 and 3 to permit the conversion of the prototype lattice of Fig. 1 to a physically realizable equivalent bridged-T network, as explained below. It comprises the series combination of an inductance L, a capacitance C and an impedance Z yet to be determined. The elements C and L have the values given by Equations 2. and 3. At

the operating frequency f0, L and C are resonant so that the impedance of Z. is equal to Z.

Fig. 5 shows the branch Z13 when N is a T-type low-pass filter made up of two series inductances L and an interposed shunt capacitance C, and Fig. 6 when N is a T-type high-pass filter constituted by two series capacitances C and an interposed shunt inductance L. Here, again,,the values of C and L are found from Equations 2 and 3.

Fig. 7 shows a specific form for the impedance Z'A suitable for use with the T-type networks of Figs.5.- and 6 to permit the realization of a physical bridged-T network equivalent to the lattice of Fig. 1. It comprises the parallel combination of a capacitance C, an inductance L and an impedance Z. The elements C and L have the values given by Equations 2 and 3.

Fig. 8 shows a bridged-T network equivalent to a lattice in which each series branch has the configuration shown in Fig. 2, each diagonal branch is an impedance EA, and Z. is of the form shown in Fig. 4. This lattice, it will be recognized, is the same as the one shown in Fig.1 except. that the branches ZA and the branchesZB are interchanged. The bridged-T network of Fig. 8 comprises two series capacitances C, an interposed shunt branch. made up of an inductance L/2 and an impedance Z/ 2 in series, and a bridging branch composed of an inductance 2L in series with a capacitance 0/2, the latter being shunted by the series combination of a second inductance 2L, a second capacitance 0/2 and an impedance 2Z. The impedance from terminal I to: terminal 3 of the bridged-T is exactly twice that of each series branch of the prototype lattice, and the impedance from terminals l and 3 taken together toterminals-2 and 4 is exactly half that of each diagonal branch of the lattice.

Fig. 9 shows, another bridged-T network which .is equivalent, at. the frequency ft, to the circuit of Fig. 8. It isderived fromv aprototype lattice in which the. network N is a high-pass retype filter, as shown in Fig. 3, and the impedance Z. has the form shown in Fig. 4.

Fig. 10 shows an unbalanced bridged-T net,- work which is the equivalent of the prototype lattice of Fig. 1 when the network N is a T-type low-pass filter, as shown in Fig. 5, and the impedance ZA hasv the configuration, shown in Fig. 7.

Thebridged-T network of Fig. 11 is similar to the one shown, in, Fig. 10 except that it is. derived from a, prototype. lattice in which the network N, is a T-type high-pass filter as shown in Fig. 6.

Each of the circuits shown in Figs. 8, 9, 10 and ll includes an impedance 2Z in the bridging branch and an impedance Z/2 in the shunt branch. In order to adjust the insertion phase of the network, these impedances are made variable, as indicated by the arrows, and for convenience may be coupled together under a single control, as indicated by the broken line connecting the arrows.

The construction and adjustment of the phase shifter can be further simplified by making the variable impedance in the bridging branch equal to the one in the shunt branch. Fig. 12 shows how the circuit of Fig. 8 may be modified to accomplish this by introducing an impedance transformation into the bridging branch. This involves taking the capacitance 0/2 out of the upper parallel arm, doubling its value, and placing it on the outside next to the capacitance 2L. The inductance 2L in the upper arm now becomes L/2 and the impedance 2Z becomes Z/2.

C. In Fig. 12 the two variable impedances Z/2 are now equal at all settings. The circuit of Fig. 12 isathe exact equivalent of the one shown in Fig.

Fig. 13 shows a further simplification that ca be made in the circuit of Fig."12 by removing the capacitance C next to the inductance 2L and reducing the value of the latter to L. At the operating frequency is an inductance L has the same impedance as the series combination of an inductance 2L and a capacitance C. That this is true is apparent from the following considerations. First, divide the inductance '2L into two equal parts, L and L. Now one inductance L will resonate with C at is and the combination will have zero reactance. Therefore, C and one of the inductances L may be removed, leaving only the other inductance L, as shown in Fig. 13 which is a preferred embodiment of the invention.

Fig. 14 shows another preferred embodiment obtained from the circuit of Fig. 9 in the same way that Fig. 13 is obtained from Fig. 8.

Figs. 15 and 16 are two other preferred embodiments of the invention obtainable by appropriate transformations of the networks of Figs. 10 and 11, respectively, in a manner analogous to that described above in connection with Figs. 12 and 13. In the circuits of Figs. and 16 the variable impedances in the bridging and shunt branches are equal but each is equal to 2Z instead of Z/2 as in the networks of Figs. 13 and 14. The networks of Figs. 15 and 16 are electrically equivalent to the prototype shown in Fig. 1.

All that remains to be determined is the .configuration of the general impedance Z. This may include only a single variable reactance, either an inductance or a capacitance. However, Z preferably comprises an inductance L1 and a capacitance C1 connected in series, as shown in Fig. 21. These preferably resonate at f0 and either or both may be variable. The series resistance R1 represents the effective resistance of the'elements L1 and C1 at f0 for an average setting of the adjustable element or elements. The shunting resistance R2 is included to compensatethe effect of the resistance R1 and its value is so chosen, as explained below, that the insertion loss of the phase shifter is substantially independent of the setting of the adjustable element.

Figs. 1'7, 18, 19 and show complete phase shifting networks in accordance withthe invention corresponding, respectively, to the circuits of Figs. 13, 14, 15 and 16 when the impedance Z has the configuration shown in Fig. 21. In. Fig. 17 the variable element in the bridging branch and the variable element in the shunt branch,

under unitary control, are the capacitances 201. In Fig. 18 these elements are the inductances L1/2, in Fig. 19 they are the capacitances C'1/2.

1'7 and 18 are equivalent to Fig. 1 if the series and diagonal branches of the lattice are interchanged.

In Fig. 1 it will be assumed that the network N hasa phase shift of90 degrees, or an odd multiple thereof, at is, that the impedance ZA has the configuration shown in Fig. 4 or Fig. '7, and that the impedance Z has the form shown in Fig; 21.

Since L and C are resonant in Fig. 4 and antiresonant in Fig. '7, the impedance Z11 will be equal to the'impedance Z at is. Therefore, in Fig.1, the insertion loss a in nepers andthe insertion phase shift 5 in radians are given by the expression a which may also be written in terms of the admittance Y as ui-i5 R,Y+1 41+ fi R.,Yl (5) where v In the case under consideration v1 1 *R. R.+1'X1 (17.)

and v v 1 X1 fo l fo 1 so we have the relation R. R, l3 R.+j 1 I ai lsfi R2 R1+jX1 Now, if we set F1 FIR.

Equation 9 may be written as 5 1 1 R, (R, R R2 +1fl:

a1, 1 R. R. 1:112-1- -from which I and l o ,3-2 tan (13) It is seen from Equation 12 that the insertion loss is independent of the value of X1 when R1 and R2 satisfy the relationship (10). Therefore. if the effective resistance R1 associated with the elements C1 andLi does not change with X1 and if the compensating resistance R2 is determined by Equation 10 the loss does not change as the phase shift 5 is varied. In practice it is found that R1 does not change appreciably as X1 is varied, especially if X1 is varied by adjusting the capacitance C1, as in Figs. 17 and 19. To minimize the change in R1 these capacitances are preferably furnished by capacitors having air as the dielectric.

From Equations 13 and 10 the following expression may be derived:

18:2 tarr g (l4) where The curve of Fig. 22 shows the'phase shift in degrees plotted against the ratio Xl/Ro'. -;If the reference phase is taken as zero when this ratio is zero, it is seen that the phase increases to +180 degrees as the ratio increases to plus infinity and decreases to 180 degrees as the ratio goes to minus infinity. If a greater phase shift is required, two or more of the phase shifters may be operated in tandem. The total phase shift of the combination will be the sum of the phase shifts of the individual networks, since the networks have a constant resistance image impedance at each end.

As an illustrative example appropriate values for the elements of the phase shifter shown in Fig. 18 will now be worked out. It will be assumed that the image impedance Ro' is 100 ohms and that a phase shift range of $90 degrees is required. If dissipation in the elements is neglected, it is necessary that the reactance X1 be adjustable from 100 ohms to +100 ohms. For

I example, the adjustable inductance L1 as shown in Fig. 21 may have a range of 900 ohms to 1100 ohms at the operating frequency f0 and the capacitance C1 in series therewith will then have a fixed reactance value of .1000 ohms at that frequency. The combination will thus vary from 100 to +100 ohms as the inductance L1 is adjusted. Now if the effective resistance R1 is 10 ohms, R0 is found from Equation to be equal to 101 ohms. From Equation 10 the proper value of the compensating resistance R2 is found to be 1010 ohms, in order to make the loss of the network independent of the phase setting. The flat loss a is found from Equation 12 to be 1.73 decibels. Now, when dissipation is taken into account, since R11 is 101 ohms the reactance change will have to be increased from $100 ohms to 101 ohms to provide the full i90-degree phase shift. In this example the elements of Fig. 18, therefore, have the following values:

and I0 is the operating frequency.

The phase shifter may, of course, be built in any of the other equivalent forms shown in Figs. 1'7, 19 and and the elements evaluated by applying the simple factors indicated. The choice of structure may be influenced, among other things, by the behavior of the network at frequencies other than the operating frequency f0. The networks shown in Figs. 18 and 20 will pass frequencies below f0 and tend to suppress frequencies above In, while the reverse is true of the networks of Figs. 17 and 19.

The phase shifters in accordance with the invention shown in Figs. 15, 16, 19 and 20 are claimed in a copending divisional application, Serial No. 187,493, filed September 29, 1950.

What is claimed is:

1. A variable phase shifter of the bridged-T type comprising two series reactances each of value X1 at the operating frequency is, an interposed shunt branch comprising a reactance of value X1/2 at f0 in series with a first general reactive impedance 2/2, a bridging branch comprising a reactance of value X1 at in and a third reactance of value X1 at f0 connected in series, and an arm connected in parallel with said third reactance of value X1 comprising a second reactance of, value X1/2 in series with a second 1 1 R2 Warm where R1/2 is the effective resistance of each of said impedances 2/2 at said frequency f0.

5. A phase shifter in accordance with claim 1 in which each of said impedances Z/2 comprises the series combination of an inductor and a capacitor.

6. A phase shifter in accordance with claim 5 in which said inductor and said capacitor are resonant at approximately the frequency is when the phase shifter is set for the mean phase shift of the range.

7. A phase shifter in accordance with claim 1 in which each of said impedances Z/2 comprises a variable capacitor.

8. A phase shifter in accordance with claim '7 in which said variable capacitors are under unitary control.

9. A phase shifter in accordance with claim 1 in which each of said impedances Z/2 comprises a variable inductor.

10. A phase shifter in accordance with claim 9 in which said variable inductors are under unitary control.

11. A phase shifter in accordance with claim 1 in which said general reactive impedances are substantially duplicates of each other.

12. A variable phase shifter of the bridged-T type comprising two series capacitors each of value 0, an interposed shunt branch comprising an inductor of value L/2 in series with a first reactive impedance Z/2, a bridging branch comprising an inductor of value L and a third capacitor of value C connected in series, and an arm connected in parallel with said third capacitor comprising a second inductor of value L/2 in series with a second reactive impedance 2/2, C and L each having at the operating frequency f0 a reactance which is equal in magnitude to the image impedance R0 of the phase shifter and said reactive impedances being adjustable and substantially equal in value.

12 in which each of said impedances Z/2 includes a resistance of value Rz/Z connected in parallel therewith approximately satisfying the relation 1 1 R2 R1 RZ R.,

where R1 is the effective resistance of each of said impedances Z/2 at said frequency in.

15. A phase shifter in accordance with claim 12 in which each of said impedances Z/2 comprises the series combination of an inductor and a capacitor.

16. A phase shifter in accordance with claim 15 in which said last-mentioned inductor and capacitor are resonant at approximately the frequency is when the phase shifter is set for the mean phase shift of the range.

17. A phase shifter in accordance with claim 12 in which said variable reactive impedances are under unitary control.

18. A variable phase shifter of the bridged-T type comprising two series inductors each of value L, an interposed shunt branch comprising a capacitor of value 20 in series with a first reactive impedance Z/2, a bridging branch comprising a capacitor of value C and a third inductor of value L connected in series, and an arm connected in parallel with said third inductor comprising a second capacitor of value 20 in series with a second reactive impedance Z/2, C and L each having at the operating frequency in a reactance which is equal in magnitude to the image impedance R0 of the phase shifter and said reactive impedances being adjustable and substantially equal in value.

19. A phase shifter in accordance with claim 18 in which said reactive impedances are substantially duplicates of each other.

20. A phase shifter in accordance with claim 18 in which each of said impedances Z/2 includes a resistance of value R2/2 connected in parallel therewith approximately satisfying the relation 1 1 R2 R R R where R1 is the effective resistance of each of said impedances 2/2 at said frequency is.

21. A phase shifter in accordance with claim 18 in which each of said impedances Z/2 comprises the series combination of an inductor and a capacitor.

22. A phase shifter in accordance with claim 18 in which said last-mentioned inductor and capacitor are resonant at approximately the frequency is when the phase shifter is set for the mean phase shift of the range.

23. A phase shifter in accordance with claim 18 in which said variable reactive impedances are under unitary control.

PAUL H. RICHARDSON.

No references cited. 

